Try a decent Sauvignon Blanc. You can pick up a decent New Zealand Marlborough region bottle for about a tenner. There is a South African called Ned which you can get from Waitrose or Majestic which is really good imho and costs about £8. If you want to pay a bit less Asda are selling a couple of decent brands for £5 at the moment. Another decent dry white would be a Pinot Grigio, you will find many Chardonnay to be slightly higher in sugar content even if they are dry, but probably not enough to make a huge difference.
If you want to try something less mainstream I love a decent bottle of Picpoul de Pinet which is from the Langedoc region of southern France.